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We provide a self-consistent electromagnetic theory of the coupling betweendipole emitters and dissipative nanoresonators. The theory that relies on theconcept of quasi-normal modes with complex frequencies provides an accurateclosed-form expression for the electromagnetic local density of states (LDOS)of any photonic or plasmonic resonator with strong radiation leakage,absorption and material dispersion. It represents a powerful tool to calculateand conceptualize the electromagnetic response of systems that are governed bya small number of resonance modes. We use the formalism to revisit Purcell'sfactor. The new formula substantially differs from the usual one; inparticular, it predicts that a spectral detuning between the emitter and theresonance does not necessarily result in a Lorentzian response in the presenceof dissipation. Comparisons with fully-vectorial numerical calculations forplasmonic nanoresonators made of gold nanorods evidence the high accuracy ofthe predictions achieved by our semi-analytical treatment.

Theory of the Spontaneous Emission in Photonic and Plasmonic Nanoresonators